I must be a few years older than you are. It was the original Cyberpunk (set in 2013, published in 1988) that did it for me.

One of the things I remember about the game was that it came with a suggested book and film list. Reading all those books, and tracking down the recommended films was something of a quest for me and my friends. That last part sounds trivial, but if your local video rental store didn't happen to have a copy of 1982's art-house weirdo indie film Liquid Sky, it was a real challenge.

Yes! and Shadowrun! I remember just binging William Gibson after that, until Johnny Mnemonic, Hackers (the movie), and Strange Days, came out. What a great decade.